## October 7, 2008

### A Distributed Bayesian Spam Filtering using Hadoop Map/Reduce

In addressing the growing problem of junk email on the Internet, I examined methods for the automated construction of filters to eliminate such unwanted messages from a user's mail stream. One was "Bayesian Spam Filtering".
Bayesian email filters take advantage of Bayes' theorem. Bayes' theorem, in the context of spam, says that the probability that an email is spam, given that it has certain words in it, is equal to the probability of finding those certain words in spam email, times the probability that any email is spam, divided by the probability of finding those words in any email:

Pr(spam|words)=Pr(words|spam)Pr(spam)/Pr(words)


In this post, I'm introduce about the implementation of a Parallel Bayesian Spam Filtering Algorithm on the distributed system (Hadoop).

1. We can get the spam probability P(wordcategory) of the words from an files of category (bad/good e-mails) as describe below:

Update: --emit <category,probability> pairs and have the reducer simply sum-up
the probabilities for a given category.

Then, it'll be more simplified. :)

Map:
    /**
* Counts word frequency
*/
public void map(LongWritable key, Text value,
OutputCollector output, Reporter reporter)
throws IOException {
String line = value.toString();
String[] tokens = line.split(splitregex);

// For every word token
for (int i = 0; i < tokens.length; i++) {
String word = tokens[i].toLowerCase();
Matcher m = wordregex.matcher(word);
if (m.matches()) {
spamTotal++;
output.collect(new Text(word), count);
}
}
}

Reduce:
    /**
* Computes bad (or good) count / total bad (or good) words
*/
public void reduce(Text key, Iterator values,
OutputCollector output, Reporter reporter)
throws IOException {
int sum = 0;
while (values.hasNext()) {
sum += (int) values.next().get();
}

output.collect(key,
new FloatWritable((float) sum / spamTotal));
}

2. We can get a rBad/rGood value of same key in each data (spam probability set of the words), We are finished adding words so finalize the results () such as a join map/reduce as describe below:
    /**
* Implement bayes rules to computer
* how likely this word is "spam"
*/
public void finalizeProb() {
if (rGood + rBad > 0)
if (pSpam < 0.01f)
pSpam = 0.01f;
else if (pSpam > 0.99f)
pSpam = 0.99f;
}


1. You probably want to smooth the estimates too (especially for zero counts ie unknown tokens).

A simple approach is "add one": for some count n, pretend you saw it n+1 times.

2. Oh, Good point, miles!! Thanks for your review. :)

3. The materials should be small and definitive, that is to say, distributed algorithm won't much help in this case. But nice example for Map/Reduce.

4. I agree with you in part that should be small and definitive, But I thought per-user based bayesian for a large-scale web-mail service, There are a lot of users. ;)

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